The Iron Law of Schools and Money

Image001There is a high correlation between the wealth of a community and the performance of its schools.

This is a partially finished chart looking at combined SAT scores of Bergen County high schools in 2009 and the median income of the town based on 2000 census figures. As the money goes up, the scores go up.

The two outliers on the bottom are towns that have expensive homes, but the kids are all shipped out to private schools. 

I omitted two towns that had median incomes in the millions. I haven't finished coding about 15 towns.

I bet if I looked at 8th grade test scores, I would find an even tighter correlation. There are many regional high schools in the area, which might combine towns of differing SES levels.

I'm walking away from the Excel worksheet for a while. Steve gave me a bug that is making the rounds at his office, and I want to sit in the sun for a half hour before the kids get home.


46 thoughts on “The Iron Law of Schools and Money

  1. Yes, it goes to 2,400 now. I was starting to feel stupid and then to feel ashamed that I still cared about my SAT percentile after more than 20 years.

  2. Do you think it is a result of the funding of the schools, or a result of the educational achievements of the parents and the level of the conversations around their dinner tables? I am never opposed to better school funding, because it is likely to help some of the kids, but I expect there are strong effects from the cohort of kids who arrive. Actually, for my large urban district, there was an analysis of test scores that accounted for SES, rating the schools for how well they did considering the experiences of kids they were enrolling. I’ll see if I can find the link.

  3. Given the information I’ve been gathering recently in re: special ed staffing in a program that’s being extended from our current prosperous school to a poor urban one, I’m guessing a critical mass of parents who have the time and energy as well as the education to oversee what’s happening in the school is also a big factor.

  4. “The Least Surprising Correlation of All Time”
    “…kids from higher income families get higher average SAT scores.
    Of course! But so what? This fact tells us nothing about the causal impact of income on test scores…
    This graph is a good example of omitted variable bias, a statistical issue discussed in Chapter 2 of my favorite textbook. The key omitted variable here is parents’ IQ. Smart parents make more money and pass those good genes on to their offspring.”

  5. Smart parents make more money and pass those good genes on to their offspring.
    Apparently, Snooki is smarter than me.

  6. I know too many poor, smart people to buy Mankiw’s argument. I don’t think that high IQ’s necessarily lead to higher incomes. I betcha that 110 from Newark leads to a smaller income than a 110 from Scarsdale.
    I find it more interesting to look at this data at a community-wide level. We moved from a so-so school to a better school when I was in sixth grade. I needed a year to catch up with the rest of the kids. I was still the same kid with the same IQ, but my skills were a year behind.
    Why do wealthier communities have better test scores? IQ might be one factor out of many. More tax revenue and PTA money. More assertive parents who know how to pressure the school. Peer group effect. Higher expectations.

  7. What’s your r^2? I give you permission (yes, you need my permission) to exclude your outliers if you have some evidence that those communities send a higher proportion of kids to private school).
    There’s a NYT “economix” blog that says the r^2 (I think, need to check if it’s r) between binned income (average in different ranges) and binned SAT is 0.95. (But, that’s not the graph you’ve done).
    I found one study that shows that the correlation between the Ravens test & SAT is 0.48 (in a college population, so w/ a limited SAT/Ravens range).
    Does anyone have a data point that correlates parental IQ with SAT scores? If one were so inclined one would try to support Rose’s hypothesis by doing multiple regressions w/ both parental IQ and parental income as regressors. One would not try to argue that parental IQ is correlated with income and income is correlated with SAT, and therefore parental IQ is correlated with SAT. Correlations aren’t transitive.
    Not sure what I’d expect to find.

  8. If one were so inclined one would try to support Rose’s hypothesis by…
    …getting 300 sets of identical twins and the world’s most drunken IRB.

  9. no r^2. I don’t have SPSS at home. I plugged some easily accessable data into EXCEL for an hour this afternoon. I’m sure that someone else has done a better job than this on a larger scale, but I need to poke around to find out.
    I’m not really comfortable dealing w/IQ stuff. It’s outside of my expertise and I don’t really trust IQ scores. I just want to look for correlations between SES and school outcomes, as part of something bigger.

  10. You can do a simple linear regression in excel. Click on graph options, add a trendline, and ask for the r^2.
    Won’t work for multiple regressions, and fancy stuff, but a simple r you can get out of the data.
    Oh, and I’m not asking for the IQ analysis — you don’t have the data for that. And, I suspect no one really does. It’s conceivable that one could get it, but only the “g” fanatics care.

  11. Ugh, I hate excel.
    They’ve moved stuff around, in the newest Mac version, but you click on the series, then the chart menu: add trendline. Then you have to got to “options” and ask for the r^2.

  12. But how can someone who doesn’t have any comfort or expertise with IQ scores be writing about SAT scores? The same discipline (psychometrics) would be required to analyze both items, and in fact IQ scores and SAT scores have a fairly high correlation. If school outcomes are the subject, I suggest using measures (e.g., graduation rates, college attendance rates) that don’t depend on psychometric data. Note that, without some psychometric analysis, which apparently isn’t going to be supplied, there is no justification for treating SAT scores as a “school outcome.”
    Everything I know on this topic I learned here:

  13. I can do that with Excel? cool. Thanks, bj.
    Yeah, I’m probably going to try coding the state standardized test scores instead of SAT scores just to avoid IQ discussions. However, I’m worried that there’s not going to be enough variation between middle class and wealthy towns. I think everyone outside of Newark scores in the 99th percentile. But I’m not sure.

  14. My husband wrote a computer program which analyzed state test scores. He was able to graphically represent the relationships between test scores (by school), gender of test takers, and family income. On a graph, many patterns pop out. His graphs showed that some schools do much better than others. It often seemed to come down to school leadership.
    At any rate, he found that, up to a median family income of $100,000, there is a strong correlation between school district results on the state tests and income. After $100,000, money makes no difference. A higher median family income does not lead to higher district test scores. We’re in the Northeast, so our cost of living should be comparable to NJ. I’d expect the income boundary to be lower in an area with a lower cost of living.

  15. Our town is in a regional district with an even wealthier town. Anecdotally, the students coming from our little, middle/middle-upper income town do better at the high school, on the whole, than the students from the wealthier town.
    Above a certain family income level, some students seem to lose track of the rewards education can bring. They may feel that they’ll be fine no matter what they do, so why sweat? Also, above a certain income level, the number of second and third marriages seems to increase.
    I will say that, at the highest income levels, there’s this odd pressure on kids. The boys should be athletes, and the girls should be beautiful. There are families who are exceptions to this rule, but it’s quite striking. (All totally anecdotal, of course!)

  16. “Yeah, I’m probably going to try coding the state standardized test scores instead of SAT scores just to avoid IQ discussions. However, I’m worried that there’s not going to be enough variation between middle class and wealthy towns. I think everyone outside of Newark scores in the 99th percentile.”
    I would be afraid of a ceiling effect with those state tests. There might not be enough headroom to really show differences at the top.
    Cranberry’s info sounds very plausible.

  17. Maybe a set of three or five dummy variables for the income groupings? If you left the middle as the omitted category, you’d see if there was a ceiling effect.

  18. That’s an interesting suggestion, that family income might show a backward-bending (or at least a tailing-off) relationship with educational performance. The scatterplot above is consistent with that suggestion.
    It’s sort of like the relationship between education and income, where more than four years of post-graduate education correlates with lower income, because (as our hostess can confirm) Ph.D.s make less than J.D.s and D.D.S.s.

  19. Ph.D.s make less than J.D.s and D.D.S.s.
    After you control for propensity to evil, that finding disappears.

  20. laura — you might want to include school expenditures for instruction in the model — my data gathering from our county shows that the poorer ses areas often have higher instructional expenditure per kid than the richer ones.
    Might also explain — rich parents can pay for SAT prep. So it might not be school prep anyhow driving those scores.

  21. Dentists are evil?
    cranberry — do you think that the income flattening might occur because of greater private school utilization? I can imagine that there’s an income threshold over which private schools become more likely.
    As I’ve mentioned we love our private school. But, we also believe that our public school is perfectly acceptable. At a different income level, our willingness to pay private school tuition for our perceived gain would drop precipitously.
    If others make that same choice, I can imagine that the public school data would be peeling off segments of the high earners, thus changing the average family income of the public school population compared to the income of the community. (I.e. Laura’s hypothesis for her “outliers” could also lead to flattening at higher income levels).
    But, what’s the goal of this analysis? I like making graphs like this a lot (hence the knowledge of how to do simple regression in XL). But which non-regressed variables are relevant confounds depends on what the goal of showing the correlation is.

  22. PS: I have to put in a plug for lawyers, too.
    The Wordle guy was recently (threatened/annoyed/harassed/questioned) with a trademark infringement concern/suit/worry, and decided to take his site down. He was inundated with lawyers offering to try to help him, and eventually found one. His post on the subject is tagged with the line “First, find the lawyers.”
    Along with corporations and hedge fund managers and oil companies, lawyers can do good as well as evil. And, Ph.D’s can do evil as well as good.

  23. Dentists are evil?
    I’ve seen “Little Shop of Horrors.”
    And, Ph.D’s can do evil as well as good.
    Yes, we had a long discussion about one that went for straight-forward evil instead of the nuanced evil you usually get from the educated classes.

  24. MH,
    My husband and I are watching The Goebbels Experiment (Kenneth Branagh reads selections from Goebbels’ diaries) and I was surprised to learn that Goebbels had a Ph.D. in drama. Who says that a doctorate in the humanities doesn’t have practical applications?

  25. bj– “do you think that the income flattening might occur because of greater private school utilization?”
    My husband used the 1999 census data for the median income stats, so it’s a reflection of the town population as a whole, rather than the free lunch statistics in the schools. Did you intend to type, “score flattening?” If so, then, no, I don’t. We’re in Massachusetts, and the distribution of private schools is different (I gather) from other parts of the country. As the public schools are held to be quite good, there are fewer private schools. There are a few very expensive, independent schools, but they draw from a wide area, in general, and they aren’t large enough to make a difference.
    You’ll also tend to see more private schools on the edge of towns whose public schools are thought to be marginal. Private schools may be more likely to depress the scores of towns which have a median income below $100,000, rather than the more affluent towns. Even there, though, I don’t think there are enough of them. I’ve read of Catholic schools shutting down due to lack of enrollment. The newspaper writers speculate that parents are not as devoted to a Catholic education as previous generations.
    And then, some of the famous private schools draw people to their towns. Some parents hope to enroll their children, eventually, in Milton Academy, or Phillips Andover, for example. Most don’t succeed in that ambition, or decide not to apply. At any rate, those schools draw families interested in education to their towns. So, do they draw the cream from the local population? I don’t think so. There are many parents who decide their children are smart enough to do well in the public schools. The town schools may even benefit from the families drawn to town by the schools.

  26. per pupil expenditures is a bad variable to use when trying to assess school quality. Poorer areas often have to spend more than middle class communities, because they have a larger number of at-risk students and special education students. (One severely affected special ed kid can really skew the numbers.) They are also in older communities with older schools that require expensive maintenance.
    It’s fun using data that is based on information that I know really well. Those two outliers on the bottom are Englewood Cliffs and Teaneck. EC is small, wealthy town that has been forced by court order to send their kids to poor, minority school in the next town over. Ergo, nearly every kid in the town goes to a private school. Teaneck is mostly poor and minority, but there’s a section of the town that has been attracted orthodox Jews who have been putting up million dollar McMansions and sending their kids to private school.
    What I love about focusing on Northern New Jersey is that all these towns range from lower middle class to upper middle class. There’s no Newark or Camden in there. And still, you can see that nice upward slope of the line. Everybody knows that the schools in middle class towns are better than the schools in Newark, but here you can see that there’s a difference between all the different shades of middle class, too.
    Cranberry, how interesting about the above $100,000 effect. Did your husband write a paper on this?

  27. Ditto to Cranberry. People hardly use private schools around here unless they live in those couple of outlier towns or are super religious or really want a lot of hand holding. Our good public schools are really good, and are better regarded than any of the private schools in the area.

  28. He’s a geek. He was noodling around, building a tool and playing with it. He started building the tool, because the administrators at our school were using the state test data in odd ways. (long story) It wasn’t their fault–there’s an entire generation of school administrators who did not need to master statistics to run schools. Suddenly, every school in the country is required to participate in producing reams of data, and live or die by the results. Culture shock resulted.
    If you knew the school as well as we, as parents did, at that time, the state tests were very good at marking weak points in the school. Unfortunately, there was a tendency on the school’s part to blame weak results on the students, rather than the school’s decisions. We had to try to explain to the administrators that you can’t claim that better results on the 8th grade test means that poor results on the 6th grade test don’t matter. They’re different tests. If your results are out of line with comparable towns on the same test, same year, you have a problem. (I’ll stop ranting. It’s an old wound.)
    At any rate, the $100,000 threshold makes sense. It’s like the effect of SES on IQ. There’s a level below which the environment has a greater effect than heredity on IQ, but above a certain level, genes have a greater effect than environment. (a quick Google found this:
    Above a certain income level, you’re less likely to move frequently. If both parents are working, the kids are in a stable care setting. The community’s prosperous enough to support the schools, even if a majority of citizens don’t have kids in the school. All sorts of good things. The real estate is stable, so the schools aren’t dealing with sudden shifts in population. Stable is good.
    However, once the environment is sufficient, more resources don’t give you a better result. Tutors can’t make normal kids into geniuses. Most parents want their children to have extracurricular activities, especially sports. And, there can be limits upon the access to advanced academic tracks at affluent high schools. Catherine Johnson at Kitchen Table Math has written at length about that. A bright kid in an affluent district, unless his parents are pushy enough to insist that he gets into the AP track, could find himself tracked out of the honors track.

  29. I’ll also note that the state tests capture the performance of just about every child in the system. Even out-placed children must take the MCAS. The SAT only captures the performance of the college-bound. Students can take the SAT many times, but they can only take each iteration of the state test once, with the exception of the 10th grade version, which they must pass for graduation.

  30. People hardly use private schools around here unless they live in those couple of outlier towns or are super religious or really want a lot of hand holding.
    Things are very different here. A quick look at the Diocese of Pittsburgh page shows 12 Catholic high schools. My area of Pittsburgh* has two of those Catholic High Schools (one boys and one girls) and several Catholic grade schools. It also has three private K-12 co-ed schools, one K-12 girls school, and a Yeshiva school.
    *The wealthier area of the city proper, maybe a circle of two or three miles in diameter.

  31. “People hardly use private schools around here unless they live in those couple of outlier towns or are super religious or really want a lot of hand holding”
    Things are very different in my neck of the woods, both our city and our neighborhood. And, as I’ve said, our schools are perfectly fine. There are some unacceptable schools in particular areas, but in vast areas of town, the schools are solid and acceptable.
    I do not understand the high degree of private school use in our neighborhoods, and have toyed with a variety of explanations, but don’t know enough about the history of the schools to have a concrete view. My favorite theory is that the choice within the public school system lad people to “shop” for schools in a way that will inevitably advantage the private schools (which get to select their students, and spend 2X as much money per student, and have 1/2 the class sizes). That is, if money isn’t relevant to one’s decision making process.

  32. That is, if money isn’t relevant to one’s decision making process.
    I think that money is part of the reasoning around here. Even many well-off people are spending around $1,000/month on housing and the parochial private schools are under $10,000 even for high schools. The public school teachers can afford private schools, which they often do use.

  33. I was just thinking of a possibility that might explain the leveling off toward the right side of Laura’s chart. At some SES level, teachers can no longer afford living in the school district, which would make working in that district less attractive.

  34. On the SES point — certainly expenditure per student is often higher where the needs are greater (or should be, at any rate). And thus is not a good measure of school excellence.
    But it does create some complexity for the mobilization argument I often here (although was not on this blog/comments, as I re-read) — that higher income areas put more money into schools, or that middle-upper class folks are more easily mobilized to pressure school districts budgets higher, leading to bigger spending for richer schools.
    Although one argument might be leveraged is that there is still this mobilization and that the expenditure for the lower SES schools needs to be even at a higher gap than there is currently.

  35. Teachers used to be required to live in the district around here (maybe just in Pittsburgh), but that stopped a few years back. The other city employees are still required to live in the city.

  36. In this state, teachers may petition their school districts to allow their children to attend school in the district. I’ve never heard of permission being denied. Some teachers petition for it, but many don’t. Teachers often know more about how a district operates than parents. A relative who’s a teacher claims it is politically difficult to teach in your home town.
    In this town, I’ve often heard the argument, “If parents would just pay a little extra for ____ , it would be much more affordable than sending the children to private school.” That’s true, as far as it goes, but the little extras add up. In other states, there are more private schools, and they are more affordable than in this state. I wonder if that would serve to restrain public school budgets? At some point, the parents may say, “Well, the private school isn’t much more than all the extra activities and supplies we support now.” In other words, the willingness to go private must be affected in some way by the cost.

  37. “If parents would just pay a little extra for ____ , it would be much more affordable than sending the children to private school.”
    I don’t think that would fly here even at a low level. Most of the private schooling is done to get an academically focused peer group.

  38. “Most of the private schooling is done to get an academically focused peer group.”
    Where I’m from, usually that’s code for “to get away from black people. Yes, I am from Long Island. My mom used to call “Our Lady of Lourdes” School “Our Lady of Malverne” because all the white families in Malverne sent their kids there.
    Anyway, that’s besides the point. My point is that the ability to send their kids to school in our district has been a perk for teachers in my district. But I think that was negotiated out of the last contract in the context of the whole residency affidavit dispute.

  39. Where I’m from, usually that’s code for “to get away from black people.”
    Around here, that is easier to do if you move to the right suburb and use public schools than if you use the Catholic schools in the city.

  40. Where I’m from, usually that’s code for “to get away from black people.”
    Hmm, in Chicago I have to confess this is sometimes true. But it’s much more frequently the case that parents are seeking a school where the problematic/disruptive-in-the-classroom kids are in small enough numbers not to overwhelm the learning environment. This often leads to kids from lower SES families not being present.
    I’m going from memory, but I believe parents are acting upon factually-based theories here … that introduction of just a couple of disruptive/troubled kids into a classroom can seriously degrade the educational experience of all. Does anyone remember this research besides me?
    FWIW, my kids’ private school is full of the children of Chicago Public Schools teachers and principals.

  41. “FWIW, my kids’ private school is full of the children of Chicago Public Schools teachers and principals.”
    I forget the numbers, but I remember hearing that Chicago is famous for the high percentage of public school teachers that send their kids to private school. Presumably, they know what they’re doing.

  42. When you consider the fact that these teachers make relatively little money (in the city, their $60-80K a year isn’t enough to buy a house, for example), and yet they scrape together enough to pony up for private school. I’m not sure what this means for Laura’s Iron Law, but it is interesting.
    Another aside: no one knows where things will land with CPS after this year. CPS is facing a combination of massive budget cuts, bad leadership at CPS, and the revocation of Chicago’s 60’s-era desegregation order earlier this school year. It will be *very* interesting to see how it all falls out.

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